Quantum mechanics

Quantum mechanics, including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, describes nature at ordinary scale. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large scale. Quantum mechanics differs from classical physics in that energy, angular momentum and other quantities of a bound system are restricted to discrete values. Quantum mechanics arose from theories to explain observations which could not be reconciled with classical physics, such as Max Planck's solution in 1900 to the black-body radiation problem, from the correspondence between energy and frequency in Albert Einstein's 1905 paper which explained the photoelectric effect. Early quantum theory was profoundly re-conceived in the mid-1920s by Erwin Schrödinger, Werner Heisenberg, Max Born and others; the modern theory is formulated in various specially developed mathematical formalisms.

In one of them, a mathematical function, the wave function, provides information about the probability amplitude of position and other physical properties of a particle. Important applications of quantum theory include quantum chemistry, quantum optics, quantum computing, superconducting magnets, light-emitting diodes, the laser, the transistor and semiconductors such as the microprocessor and research imaging such as magnetic resonance imaging and electron microscopy. Explanations for many biological and physical phenomena are rooted in the nature of the chemical bond, most notably the macro-molecule DNA. Scientific inquiry into the wave nature of light began in the 17th and 18th centuries, when scientists such as Robert Hooke, Christiaan Huygens and Leonhard Euler proposed a wave theory of light based on experimental observations. In 1803, Thomas Young, an English polymath, performed the famous double-slit experiment that he described in a paper titled On the nature of light and colours.

This experiment played a major role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays; these studies were followed by the 1859 statement of the black-body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system can be discrete, the 1900 quantum hypothesis of Max Planck. Planck's hypothesis that energy is radiated and absorbed in discrete "quanta" matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, known as Wien's law in his honor. Ludwig Boltzmann independently arrived at this result by considerations of Maxwell's equations. However, it underestimated the radiance at low frequencies. Planck corrected this model using Boltzmann's statistical interpretation of thermodynamics and proposed what is now called Planck's law, which led to the development of quantum mechanics. Following Max Planck's solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect.

Around 1900–1910, the atomic theory and the corpuscular theory of light first came to be accepted as scientific fact. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, Pieter Zeeman, each of whom has a quantum effect named after him. Robert Andrews Millikan studied the photoelectric effect experimentally, Albert Einstein developed a theory for it. At the same time, Ernest Rutherford experimentally discovered the nuclear model of the atom, for which Niels Bohr developed his theory of the atomic structure, confirmed by the experiments of Henry Moseley. In 1913, Peter Debye extended Niels Bohr's theory of atomic structure, introducing elliptical orbits, a concept introduced by Arnold Sommerfeld; this phase is known as old quantum theory. According to Planck, each energy element is proportional to its frequency: E = h ν, where h is Planck's constant. Planck cautiously insisted that this was an aspect of the processes of absorption and emission of radiation and had nothing to do with the physical reality of the radiation itself.

In fact, he considered his quantum hypothesis a mathematical trick to get the right answer rather than a sizable discovery. However, in 1905 Albert Einstein interpreted Planck's quantum hypothesis realistically and used it to explain the photoelectric effect, in which shining light on certain materials can eject electrons from the material, he won the 1921 Nobel Prize in Physics for this work. Einstein further developed this idea to show that an electromagnetic wave such as light could be described as a particle, with a discrete quantum of energy, dependent on its frequency; the foundations of quantum mechanics were established during the first half of the 20th century by Max Planck, Niels Bohr, Werner Heisenberg, Louis de Broglie, Arthur Compton, Albert Einstein, Erwin Schrödinger, Max Born, John von Neumann, Paul Dirac, Enrico Fermi, Wolfgang Pauli, Max von Laue, Freeman Dyson, David Hilbert, Wi

Condensed matter physics

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is large and the interactions between the constituents are strong; the most familiar examples of condensed phases are solids and liquids, which arise from the electromagnetic forces between atoms. Condensed matter physicists seek to understand the behavior of these phases by using physical laws. In particular, they include the laws of quantum mechanics and statistical mechanics; the most familiar condensed phases are solids and liquids while more exotic condensed phases include the superconducting phase exhibited by certain materials at low temperature, the ferromagnetic and antiferromagnetic phases of spins on crystal lattices of atoms, the Bose–Einstein condensate found in ultracold atomic systems. The study of condensed matter physics involves measuring various material properties via experimental probes along with using methods of theoretical physics to develop mathematical models that help in understanding physical behavior.

The diversity of systems and phenomena available for study makes condensed matter physics the most active field of contemporary physics: one third of all American physicists self-identify as condensed matter physicists, the Division of Condensed Matter Physics is the largest division at the American Physical Society. The field overlaps with chemistry, materials science, nanotechnology, relates to atomic physics and biophysics; the theoretical physics of condensed matter shares important concepts and methods with that of particle physics and nuclear physics. A variety of topics in physics such as crystallography, elasticity, etc. were treated as distinct areas until the 1940s, when they were grouped together as solid state physics. Around the 1960s, the study of physical properties of liquids was added to this list, forming the basis for the new, related specialty of condensed matter physics. According to physicist Philip Warren Anderson, the term was coined by him and Volker Heine, when they changed the name of their group at the Cavendish Laboratories, Cambridge from Solid state theory to Theory of Condensed Matter in 1967, as they felt it did not exclude their interests in the study of liquids, nuclear matter, so on.

Although Anderson and Heine helped popularize the name "condensed matter", it had been present in Europe for some years, most prominently in the form of a journal published in English and German by Springer-Verlag titled Physics of Condensed Matter, launched in 1963. The funding environment and Cold War politics of the 1960s and 1970s were factors that lead some physicists to prefer the name "condensed matter physics", which emphasized the commonality of scientific problems encountered by physicists working on solids, liquids and other complex matter, over "solid state physics", associated with the industrial applications of metals and semiconductors; the Bell Telephone Laboratories was one of the first institutes to conduct a research program in condensed matter physics. References to "condensed" state can be traced to earlier sources. For example, in the introduction to his 1947 book Kinetic Theory of Liquids, Yakov Frenkel proposed that "The kinetic theory of liquids must accordingly be developed as a generalization and extension of the kinetic theory of solid bodies.

As a matter of fact, it would be more correct to unify them under the title of'condensed bodies'". One of the first studies of condensed states of matter was by English chemist Humphry Davy, in the first decades of the nineteenth century. Davy observed that of the forty chemical elements known at the time, twenty-six had metallic properties such as lustre and high electrical and thermal conductivity; this indicated that the atoms in John Dalton's atomic theory were not indivisible as Dalton claimed, but had inner structure. Davy further claimed that elements that were believed to be gases, such as nitrogen and hydrogen could be liquefied under the right conditions and would behave as metals. In 1823, Michael Faraday an assistant in Davy's lab liquefied chlorine and went on to liquefy all known gaseous elements, except for nitrogen and oxygen. Shortly after, in 1869, Irish chemist Thomas Andrews studied the phase transition from a liquid to a gas and coined the term critical point to describe the condition where a gas and a liquid were indistinguishable as phases, Dutch physicist Johannes van der Waals supplied the theoretical framework which allowed the prediction of critical behavior based on measurements at much higher temperatures.

By 1908, James Dewar and Heike Kamerlingh Onnes were able to liquefy hydrogen and newly discovered helium, respectively. Paul Drude in 1900 proposed the first theoretical model for a classical electron moving through a metallic solid. Drude's model described properties of metals in terms of a gas of free electrons, was the first microscopic model to explain empirical observations such as the Wiedemann–Franz law. However, despite the success of Drude's free electron model, it had one notable problem: it was unable to explain the electronic contribution to the specific heat and magnetic properties of metals, the temperature dependence of resistivity at low temperatures. In 1911, three years after helium was first liquefied, Onnes working at University of Leiden discovered superconductivity in mercury, when he observed the electrical resistivity of mercury to vanish at temperatures below a certain value; the phenomenon surprised the best theoretical physicists of the time, it remain

ArXiv

ArXiv is a repository of electronic preprints approved for posting after moderation, but not full peer review. It consists of scientific papers in the fields of mathematics, astronomy, electrical engineering, computer science, quantitative biology, mathematical finance and economics, which can be accessed online. In many fields of mathematics and physics all scientific papers are self-archived on the arXiv repository. Begun on August 14, 1991, arXiv.org passed the half-million-article milestone on October 3, 2008, had hit a million by the end of 2014. By October 2016 the submission rate had grown to more than 10,000 per month. ArXiv was made possible by the compact TeX file format, which allowed scientific papers to be transmitted over the Internet and rendered client-side. Around 1990, Joanne Cohn began emailing physics preprints to colleagues as TeX files, but the number of papers being sent soon filled mailboxes to capacity. Paul Ginsparg recognized the need for central storage, in August 1991 he created a central repository mailbox stored at the Los Alamos National Laboratory which could be accessed from any computer.

Additional modes of access were soon added: FTP in 1991, Gopher in 1992, the World Wide Web in 1993. The term e-print was adopted to describe the articles, it began as a physics archive, called the LANL preprint archive, but soon expanded to include astronomy, computer science, quantitative biology and, most statistics. Its original domain name was xxx.lanl.gov. Due to LANL's lack of interest in the expanding technology, in 2001 Ginsparg changed institutions to Cornell University and changed the name of the repository to arXiv.org. It is now hosted principally with eight mirrors around the world, its existence was one of the precipitating factors that led to the current movement in scientific publishing known as open access. Mathematicians and scientists upload their papers to arXiv.org for worldwide access and sometimes for reviews before they are published in peer-reviewed journals. Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv; the annual budget for arXiv is $826,000 for 2013 to 2017, funded jointly by Cornell University Library, the Simons Foundation and annual fee income from member institutions.

This model arose in 2010, when Cornell sought to broaden the financial funding of the project by asking institutions to make annual voluntary contributions based on the amount of download usage by each institution. Each member institution pledges a five-year funding commitment to support arXiv. Based on institutional usage ranking, the annual fees are set in four tiers from $1,000 to $4,400. Cornell's goal is to raise at least $504,000 per year through membership fees generated by 220 institutions. In September 2011, Cornell University Library took overall administrative and financial responsibility for arXiv's operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it "was supposed to be a three-hour tour, not a life sentence". However, Ginsparg remains on the arXiv Scientific Advisory Board and on the arXiv Physics Advisory Committee. Although arXiv is not peer reviewed, a collection of moderators for each area review the submissions; the lists of moderators for many sections of arXiv are publicly available, but moderators for most of the physics sections remain unlisted.

Additionally, an "endorsement" system was introduced in 2004 as part of an effort to ensure content is relevant and of interest to current research in the specified disciplines. Under the system, for categories that use it, an author must be endorsed by an established arXiv author before being allowed to submit papers to those categories. Endorsers are not asked to review the paper for errors, but to check whether the paper is appropriate for the intended subject area. New authors from recognized academic institutions receive automatic endorsement, which in practice means that they do not need to deal with the endorsement system at all. However, the endorsement system has attracted criticism for restricting scientific inquiry. A majority of the e-prints are submitted to journals for publication, but some work, including some influential papers, remain purely as e-prints and are never published in a peer-reviewed journal. A well-known example of the latter is an outline of a proof of Thurston's geometrization conjecture, including the Poincaré conjecture as a particular case, uploaded by Grigori Perelman in November 2002.

Perelman appears content to forgo the traditional peer-reviewed journal process, stating: "If anybody is interested in my way of solving the problem, it's all there – let them go and read about it". Despite this non-traditional method of publication, other mathematicians recognized this work by offering the Fields Medal and Clay Mathematics Millennium Prizes to Perelman, both of which he refused. Papers can be submitted in any of several formats, including LaTeX, PDF printed from a word processor other than TeX or LaTeX; the submission is rejected by the arXiv software if generating the final PDF file fails, if any image file is too large, or if the total size of the submission is too large. ArXiv now allows one to store and modify an incomplete submission, only finalize the submission when ready; the time stamp on the article is set. The standard access route is through one of several mirrors. Sev

Sidney Coleman

Sidney Richard Coleman was an American theoretical physicist who studied under Murray Gell-Mann. He is noted for his research in high-energy theoretical physics. Sidney Coleman grew up on the Far North Side of Chicago. In 1957, he received his undergraduate degree from the Illinois Institute of Technology physics department, he received his Ph. D. under Murray Gell-Mann from the California Institute of Technology in 1962 and moved to Harvard University that year, where he spent his entire career, meeting his wife Diana there in the late 1970s. They were married in 1982. "He was a giant in a peculiar sense, because he's not known to the general populace," Nobel laureate Sheldon Glashow told the Boston Globe. "He's not a Stephen Hawking. But within the community of theoretical physicists, he's kind of a major god, he is the physicist's physicist."In 1966, Antonino Zichichi recruited Coleman as a lecturer at the then-new summer school at International School for Subnuclear Physics in Erice, Sicily.

A legendary figure at the school throughout the 1970s and early 1980s, Coleman was awarded the title "Best Lecturer" on the occasion of the school's fifteenth anniversary. His explanation of spontaneous symmetry breaking in terms of a little man living inside a ferromagnet has been cited by popularizers; the classic particle physics text Aspects of Symmetry is a collection of Coleman's lectures at Erice. A quote from his introduction to the book is worth sharing here: I first came to Erice in 1966, to lecture at the fourth of the annual schools on subnuclear physics organized by Nino Zichichi. I was charmed by the beauty of Erice, fascinated by the thick layers of Sicilian culture and history, terrified by the iron rule with which Nino kept the students and faculty in line. In a word, I was won over, I returned to Erice every year or two thereafter, to talk of what was past, or passing, or to come, at least insofar as it touched on subnuclear theory…These lectures span fourteen years, from 1966 to 1979.

This was a great time to be a high-energy theorist, the period of the famous triumph of quantum field theory. And what a triumph it was, in the old sense of the word: a glorious victory parade, full of wonderful things brought back from far places to make the spectator gasp with awe and laugh with joy. I hope some of that joy has been captured here. Coleman's lectures at Harvard were legendary. Students in one quantum field theory course created T-shirts bearing his image and a collection of his more noted quotations, among them: "Not only God knows, I know, by the end of the semester, you will know." Despite this acclaim, he did not enjoy teaching or mentoring graduate students: I hate. You do it as part of the job. Well, that's of course false... or maybe more true than false when I say I hate it.... But I would be just as happy if I had no graduate students.... There is a graduate student, a joy to collaborate with. Both David Politzer and Erick Weinberg were of this kind, but they were almost mature physicists.

They were bright by the time they came to me. In general, working with a graduate student is like teaching a course. It's unpleasant work. A pain in the neck. You do it. If I weren't paid to do it I would never do it. In 1989, Coleman was awarded the NAS Award for Scientific Reviewing from the National Academy of Sciences; that award praised his "lucid and influential reviews on conserved currents, gauge theories and magnetic monopoles--subjects fundamental to theoretical physics." In 2005, Harvard University's physics department held the "SidneyFest", a conference on quantum field theory and quantum chromodynamics, organized in his honor. Aside from his academic work, Coleman was a prominent science fiction enthusiast, he was one of the founders of Advent: Publishers and reviewed genre books for The Magazine of Fantasy and Science Fiction. Some of his best known works are Coleman–Mandula theorem Tadpoles Coleman theorem Equivalence of the Thirring model and the quantum sine-Gordon equation Semiclassical analysis of the fate of a false vacuum Coleman–Weinberg potential Q-balls in the thin-wall limit Lectures at Erice, some of which are preserved in his book Aspects of Symmetry Sidneyfest - physicists' celebration of Sidney Coleman's life Chicago Tribune obituary, November 20, 2007.

Harvard Gazette obituary, November 29, 2007. Boston Globe obituary, January 20, 2008. Physics Today May 2008, written by Sheldon Glashow. "Quantum Mechanics In Your Face", A lecture by Prof. Coleman at the New England sectional meeting of the American Physical Society April 9, 1994. Physics 253: Quantum Field Theory. Video of lectures by Sidney Coleman at Harvard in 1975-1976. Sidney Coleman at the Mathematics Genealogy Project National Academy of Sciences Biographical Memoir

Boson

In quantum mechanics, a boson is a particle that follows Bose–Einstein statistics. Bosons make up one of the two classes of the other being fermions; the name boson was coined by Paul Dirac to commemorate the contribution of Indian physicist and professor of physics at University of Calcutta and at University of Dhaka, Satyendra Nath Bose in developing, with Albert Einstein, Bose–Einstein statistics—which theorizes the characteristics of elementary particles. Examples of bosons include fundamental particles such as photons, W and Z bosons, the discovered Higgs boson, the hypothetical graviton of quantum gravity; some composite particles are bosons, such as mesons and stable nuclei of mass number such as deuterium, helium-4, or lead-208. An important characteristic of bosons is that their statistics do not restrict the number of them that occupy the same quantum state; this property is exemplified by helium-4. Unlike bosons, two identical fermions cannot occupy the same quantum space. Whereas the elementary particles that make up matter are fermions, the elementary bosons are force carriers that function as the'glue' holding matter together.

This property holds for all particles with integer spin as a consequence of the spin–statistics theorem. When a gas of Bose particles is cooled down to temperatures close to absolute zero the kinetic energy of the particles decreases to a negligible amount, they condense into the lowest energy level state; this state is called a Bose-Einstein condensate. It is believed. Bosons may be composite, like mesons. While most bosons are composite particles, in the Standard Model of Particle Physics there are five bosons which are elementary: the Standard Model requires one scalar boson H0 Higgs bosonthe four vector bosons that are the gauge bosons for the Standard Model:γ Photon g Gluons Z Neutral weak boson W± Charged weak bosons There may be a sixth tensor boson, the graviton, that would be the force-carrier for gravity, it remains a hypothetical elementary particle since all attempts so far to incorporate gravitation into the Standard Model have failed. If the graviton does exist, it must be a boson, could conceivably be a gauge boson.

Composite bosons, such as helium nuclei, are important in superfluidity and other applications of Bose–Einstein condensates. Bosons differ from fermions. Two or more identical fermions cannot occupy the same quantum state. Since bosons with the same energy can occupy the same place in space, bosons are force carrier particles, including composite bosons such as mesons. Fermions are associated with matter. Bosons are particles which obey Bose–Einstein statistics: When one swaps two bosons, the wavefunction of the system is unchanged. Fermions, on the other hand, obey Fermi–Dirac statistics and the Pauli exclusion principle: Two fermions cannot occupy the same quantum state, accounting for the "rigidity" or "stiffness" of matter which includes fermions, thus fermions are sometimes said to be the constituents of matter, while bosons are said to be the particles that transmit interactions, or the constituents of radiation. The quantum fields of bosons are bosonic fields; the properties of lasers and masers, superfluid helium-4 and Bose–Einstein condensates are all consequences of statistics of bosons.

Another result is that the spectrum of a photon gas in thermal equilibrium is a Planck spectrum, one example of, black-body radiation. Interactions between elementary particles are called fundamental interactions; the fundamental interactions of virtual bosons with real particles result. All known elementary and composite particles are bosons or fermions, depending on their spin: Particles with half-integer spin are fermions. In the framework of nonrelativistic quantum mechanics, this is a purely empirical observation. In relativistic quantum field theory, the spin–statistics theorem shows that half-integer spin particles cannot be bosons and integer spin particles cannot be fermions. In large systems, the difference between bosonic and fermionic statistics is only apparent at large densities — when their wave functions overlap. At low densities, both types of statistics are well approximated by Maxwell–Boltzmann statistics, described by classical mechanics. All observed elementary particles bosons.

The observed elementary bosons are all gauge bosons: photons, W and Z bosons, except the Higgs boson, a scalar boson. Photons are the force carriers of the electromagnetic field. W and Z bosons are the force carriers. Gluons are the fundamental force carriers underlying the strong force. Higgs bosons give Z bosons mass via the Higgs mechanism, their existence was confirmed by CERN on 14 March 2013. Many approaches to quantum gravity postulate a force carrier for gravity, the graviton, a boson of spin plus or minus two. Composite particles can be b

Fermion

In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. These particles obey the Pauli exclusion principle. Fermions include all quarks and leptons, as well as all composite particles made of an odd number of these, such as all baryons and many atoms and nuclei. Fermions differ from bosons. A fermion can be an elementary particle, such as the electron, or it can be a composite particle, such as the proton. According to the spin-statistics theorem in any reasonable relativistic quantum field theory, particles with integer spin are bosons, while particles with half-integer spin are fermions. In addition to the spin characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is referred to as the spin statistics relation is in fact a spin statistics-quantum number relation; as a consequence of the Pauli exclusion principle, only one fermion can occupy a particular quantum state at any given time. If multiple fermions have the same spatial probability distribution at least one property of each fermion, such as its spin, must be different.

Fermions are associated with matter, whereas bosons are force carrier particles, although in the current state of particle physics the distinction between the two concepts is unclear. Weakly interacting fermions can display bosonic behavior under extreme conditions. At low temperature fermions show superfluidity for uncharged particles and superconductivity for charged particles. Composite fermions, such as protons and neutrons, are the key building blocks of everyday matter; the name fermion was coined by English theoretical physicist Paul Dirac from the surname of Italian physicist Enrico Fermi. The Standard Model recognizes two types of elementary fermions: leptons. In all, the model distinguishes 24 different fermions. There are six quarks, six leptons, along with the corresponding antiparticle of each of these. Mathematically, fermions come in three types: Weyl fermions, Dirac fermions, Majorana fermions. Most Standard Model fermions are believed to be Dirac fermions, although it is unknown at this time whether the neutrinos are Dirac or Majorana fermions.

Dirac fermions can be treated as a combination of two Weyl fermions. In July 2015, Weyl fermions have been experimentally realized in Weyl semimetals. Composite particles can be fermions depending on their constituents. More because of the relation between spin and statistics, a particle containing an odd number of fermions is itself a fermion, it will have half-integer spin. Examples include the following: A baryon, such as the proton or neutron, contains three fermionic quarks and thus it is a fermion; the nucleus of a carbon-13 atom is therefore a fermion. The atom helium-3 is made of two protons, one neutron, two electrons, therefore it is a fermion; the number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion. Fermionic or bosonic behavior of a composite particle is only seen at large distances. At proximity, where spatial structure begins to be important, a composite particle behaves according to its constituent makeup.

Fermions can exhibit bosonic behavior. This is the origin of superconductivity and the superfluidity of helium-3: in superconducting materials, electrons interact through the exchange of phonons, forming Cooper pairs, while in helium-3, Cooper pairs are formed via spin fluctuations; the quasiparticles of the fractional quantum Hall effect are known as composite fermions, which are electrons with an number of quantized vortices attached to them. In a quantum field theory, there can be field configurations of bosons which are topologically twisted; these are coherent states which behave like a particle, they can be fermionic if all the constituent particles are bosons. This was discovered by Tony Skyrme in the early 1960s, so fermions made of bosons are named skyrmions after him. Skyrme's original example involved fields which take values on a three-dimensional sphere, the original nonlinear sigma model which describes the large distance behavior of pions. In Skyrme's model, reproduced in the large N or string approximation to quantum chromodynamics, the proton and neutron are fermionic topological solitons of the pion field.

Whereas Skyrme's example involved pion physics, there is a much more familiar example in quantum electrodynamics with a magnetic monopole. A bosonic monopole with the smallest possible magnetic charge and a bosonic version of the electron will form a fermionic dyon; the analogy between the Skyrme field and the Higgs field of the electroweak sector has been used to postulate that all fermions are skyrmions. This could explain why all known fermions have baryon or lepton quantum numbers and provide a physical mechanism for the Pauli exclusion principle

Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize and predict natural phenomena. This is in contrast to experimental physics; the advancement of science depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations. For example, while developing special relativity, Albert Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was uninterested in the Michelson–Morley experiment on Earth's drift through a luminiferous aether. Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect an experimental result lacking a theoretical formulation. A physical theory is a model of physical events, it is judged by the extent. The quality of a physical theory is judged on its ability to make new predictions which can be verified by new observations.

A physical theory differs from a mathematical theorem in that while both are based on some form of axioms, judgment of mathematical applicability is not based on agreement with any experimental results. A physical theory differs from a mathematical theory, in the sense that the word "theory" has a different meaning in mathematical terms. A physical theory involves one or more relationships between various measurable quantities. Archimedes realized that a ship floats by displacing its mass of water, Pythagoras understood the relation between the length of a vibrating string and the musical tone it produces. Other examples include entropy as a measure of the uncertainty regarding the positions and motions of unseen particles and the quantum mechanical idea that energy are not continuously variable. Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms a good example. For instance: "phenomenologists" might employ empirical formulas to agree with experimental results without deep physical understanding.

"Modelers" appear much like phenomenologists, but try to model speculative theories that have certain desirable features, or apply the techniques of mathematical modeling to physics problems. Some attempt to create approximate theories, called effective theories, because developed theories may be regarded as unsolvable or too complicated. Other theorists may try to unify, reinterpret or generalise extant theories, or create new ones altogether. Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled. Theoretical problems that need computational investigation are the concern of computational physics. Theoretical advances may consist in setting aside old, incorrect paradigms or may be an alternative model that provides answers that are more accurate or that can be more applied. In the latter case, a correspondence principle will be required to recover the known result. Sometimes though, advances may proceed along different paths. For example, an correct theory may need some conceptual or factual revisions.

However, an exception to all the above is the wave–particle duality, a theory combining aspects of different, opposing models via the Bohr complementarity principle. Physical theories become accepted if they are able to make correct predictions and no incorrect ones; the theory should have, at least as a secondary objective, a certain economy and elegance, a notion sometimes called "Occam's razor" after the 13th-century English philosopher William of Occam, in which the simpler of two theories that describe the same matter just as adequately is preferred. They are more to be accepted if they connect a wide range of phenomena. Testing the consequences of a theory is part of the scientific method. Physical theories can be grouped into three categories: mainstream theories, proposed theories and fringe theories. Theoretical physics began at least 2,300 years ago, under the Pre-socratic philosophy, continued by Plato and Aristotle, whose views held sway for a millennium. During the rise of medieval universities, the only acknowledged intellectual disciplines were the seven liberal arts of the Trivium like grammar and rhetoric and of the Quadrivium like arithmetic, geometry and astronomy.

During the Middle Ages and Renaissance, the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon. As the Scientific Revolution gathered pace, the concepts of matter, space and causality began to acquire the form we know today, other sciences spun off from the rubric of natural philosophy, thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe.